Manipulating formulae (1)

AGENDA
Objectives

Page Numbers

Expand and factorise given expressions

56-59

Substitute values into formulae and solve for variables 92-93
Change the subject of a formula

105-107

Manipulating Formulae


Expand
Multiply every term inside the brackets by the term outside:

3(5+2)
= 3 × 5+ 3 × 2
= 15 + 6


Expand
Multiply both terms inside the first brackets by both terms inside
the second brackets:

( + 4)( - 2)

=

2

-2 +4 -8
2

= +2-8


Expand
Multiply both terms inside the first brackets by both terms inside
the second brackets:

( + 3)( - 3)
=

2

+3 -3 -9
2

= -9


Expand
Multiply both terms inside the first brackets by both terms inside
the second brackets:
2

( - 6)

= ( - 6)(x - 6)
=

2

-6 -6 +36
2


Textbook Activity

Expand & Simplify
Turn to page 62
Complete Q7-11


p62 Q7-11
a) x2 + 9x + 14
b) x2 + 3x - 40

c) x2 + 2x - 24
d) x2 - 16x + 63

No. (x - 6)2 = x2 - 12x + 36
x2 - 4
x2 - 49
x2 + 10x + 25

p62 Q7-11
2x2 - 9x - 18
6x2 + x - 40
12x2 - 41x + 24
4x2 - 49

(2x + 1)(3x - 2) = 6x2 - x -2


Factorise
x2 - 4x - 45
Let’s think of the expression as ax2 + bx + c.
We must find 2 numbers that:
have product (x) = c
have sum (+) = b


Factorise
x2 - 4x - 45
ax2 + bx + c
product (x) = -45
sum (+) = -4
Can you think of 2 numbers that work?


Factorise
x2 - 4x - 45
product (x) = -45
sum (+) = -4

-9 and +5, we can show the answer as
(x - 9)(x + 5)


Factorise
x2 + 6x - 7
product (x) = -7
sum (+) = 6
-1 and +7, we can show the answer as
(x - 1)(x + 7)


Factorise
x2 - 16
product (x) = -16
sum (+) = 0
-4 and +4, we can show the answer as
(x - 4)(x + 4)


Textbook Activity

Factorising
Turn to page 63
Complete Q12-14


p63 Q12-14
(x + 2)(x + 3)
(x + 9)(x - 2)

(x - 1)(x - 4)
(x + 5)(x - 9)
(x + 3)2
(x - 5)2
(x + 7)(x - 7)

(x - 7)(x + 3)


Reverse algebraic operation!


ALBERT THE ASTRONAUT
It is essential that during training
astronauts are able to calculate the
velocity (v) required to ensure the
necessary lift (L).
Rearrange this equation to help
Albert find the velocity.


Things to remember
• Follow BODMAS in reverse.
Add/subtract, multiply/divide,
powers/roots, brackets
• Whatever you do to one side of the
equation you must do to the other.
• If you're making x the subject it means
that this is the only x in your answer.

Example 1 (simple)
Make t the subject of the formula: r = k - ct
+ct

+ct

r + ct = k
-r

-r

ct = k - r
÷c

t= k-r
c

÷c

k
r
Answer: t =
c